Market Weights: Why Producers Choose the Wrong Weight

:     The profit maximizing market weight for pigs is a function of the price received and the costs remaining at the time of the projection.  If you think of a single pig (the simplest case) near the end of finishing, the cost remaining is the last finishing diet.  The decision revolves around estimating the marginal cost of an additional pound and the marginal revenue of that additional pound from the packer.

     The marginal cost is the change in total cost divided by the change in output.  From that formula you can see that no fixed costs enter this calculation.  As the pig grows during the final finishing phase, its marginal feed efficiency is getting worse and in most cases, the lean percent is declining while the yield may be rising slightly.  Both typically impact price paid.  On the other hand, the marginal revenue is typically a step function (rather than continous) and is poised to jump down as the next level of sort loss is overtaken.

     So in the final week(s) the cost is rising per pound and the price received is falling.  As long as the next increment of revenue exceeds the cost of that additional pound, the next pound should be added.

     In practice, many producers do this calculation on the back of an envelope and come up with a number.  The problem is that we do not sell pigs one at a time and therefore the group which is marketed must be taken into account.  By failing to do so, the typical producer overestimates the profit maximizing final weight.

     In reality, every pig in the barn is growing according to its own "growth curve" and "average daily feed intake function" though we typically estimate these with an average.  When you consider a marketing group of 180 pigs (the typical truck load), even after careful selection, the group has an average and a variance.  On such a load, the producer who has calculated the single pig optimum usually sets the load average to this result.  

     The problem is that the leading edge of this 180 head will invariably be into some pretty heavy sort loss by the time the average weight equals the single pig optimum.  The effect is not symetrical since the below average weight group is usually well into the prime part of the matrix.  When you calculate the profit optimizing average market weight of the group vs. the single pig, the optimal group average weight, the weight which maximizes the profits of the load, will be well below (often 10 or more lbs) the single pig number.  This is especially the case when feed costs are high and market prices below average.

     As the variance of weights on the loads decreases, the load optimum weight rises to approach the single pig optimum and as you can imagine, if the variance is reduced to zero, the load optimum becomes the single pig optimum.  The wider the variance, all things equal, the lower the average optimum load weight will be compared to the single pig optimum.

     We can take this to the building and site level but the same principles apply.  When there is variance, the profit optimal load weight falls compared to the single pig case.

     Some numbers on this next time...